• Title/Summary/Keyword: gradation of openness

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L-FUZZY GRADATION OF OPENNESS AND L-FUZZY GRADATION OF PROXIMITY

  • Mondal Taras Kumar;Samanta S.K.
    • The Pure and Applied Mathematics
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    • v.13 no.2 s.32
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    • pp.71-94
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    • 2006
  • In this paper we study lattice valued fuzzy gradation of openness so that fuzzy gradation of openness [13] could be obtained as a particular case. Some of its properties are studied. We also give definitions of lattice valued graded fuzzy filters, graded, fuzzy grills, graded fuzzy preproximities and proximities.

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SOME RESULTS ON INTUITIONISTIC FUZZY TOPOLOGICAL SPACES DEFINED BY INTUITIONISTIC GRADATION OF OPENNESS

  • MIN WON KEUN;PARK CHUN-KEE
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.791-801
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    • 2005
  • In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

On Intuitionistic Fuzzy Generalized Topological Spaces (Intuitionistic Fuzzy Generalized Topological Spaces 관한 연구)

  • Min, Won-Keun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.19 no.5
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    • pp.725-729
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    • 2009
  • In this paper, we introduce the concepts of intuitionistic fuzzy generalized topological spaces and intuitionistic gradation of generalized openness. We also introduce the concepts of IFG-mapping, weak IFG-mapping and IFG-open mapping, and obtain some characterizations for such mappings.

FUZZY CONVERGENCE THEORY - I

  • MONDAL K. K.;SAMANTA S. K.
    • The Pure and Applied Mathematics
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    • v.12 no.1
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    • pp.75-91
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    • 2005
  • The main objective of this paper is to introduce the gradation of neigh-bourhoodness in L-fuzzy topology and to introduce the fuzziness in the concept of convergence of L-fuzzy nets.

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INTERVAL-VALUED SMOOTH TOPOLOGICAL SPACES

  • Choi, Jeong-Yeol;Kim, So-Ra;Hur, Kul
    • Honam Mathematical Journal
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    • v.32 no.4
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    • pp.711-738
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    • 2010
  • We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

SOME RESULTS ON AN INTUITIONISTIC FUZZY TOPOLOGICAL SPACE

  • Min, Kyung-Ho;Min, Won Keun;Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.14 no.1
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    • pp.57-64
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    • 2006
  • In this paper, we introduce the concepts of $r$-closure and $r$-interior defined by intuitionistic gradation of openness. We also introduce the concepts of $r$-gp-maps, weakly $r$-gp-maps, and obtain some characterizations in terms of $r$-closure and $r$-interior operators.

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HALF-GP-MAPS ON INTUITIONISTIC FUZZY TOPOLOGICAL SPACES

  • Min, Won Keun;Park, Chun-Kee;Min, Kyung-Ho
    • Korean Journal of Mathematics
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    • v.12 no.2
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    • pp.177-183
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    • 2004
  • In this paper, we introduce the concepts of half-interior, half-closure, half-gp-maps and half-gp-open maps defined by intuitionistic gradations of openness.

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SEVERAL TYPES FUZZY HALF-COMPACTNESS ON AN INTUITIONISTIC FUZZY TOPOLOGICAL SPACE

  • Min, Kvung-Ho;Min, Won Keun;Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.13 no.2
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    • pp.249-254
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    • 2005
  • In this paper, we introduce the concepts of intuitionistic fuzzy half-compactness, nearly intuitionistic fuzzy half-compactness and almost intuitionistic fuzzy half-compactness defined by intuitionistic gradations of openness, and obtain some characterizations.

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